Upscaling Mixing-Controlled Reactions in Unsaturated Porous Media.

We study mixing-controlled chemical reactions in unsaturated porous media from a pore-scale perspective. The spatial heterogeneity induced by the presence of two immiscible phases, here water and air, in the pore space generates complex flow patterns that dominate reactive mixing across scales. To assess the impact of different macroscopic saturation states (the fraction of pore volume occupied by water) on mixing-controlled chemical reactions, we consider a fast irreversible reaction between two initially segregated dissolved species that mix as one solution displaces the other in the heterogeneous flow field of the water phase. We use the pore-scale geometry and water distributions from the laboratory experiments reported by Jiménez-Martínez et al. (Geophys. Res. Lett. 42: 5316-5324, 2015). We analyze reactive mixing in three complementary ways. Firstly, we post-process experimentally observed spatially distributed concentration data; secondly, we perform numerical simulations of flow and reactive transport in the heterogeneous water phase, and thirdly, we use an upscaled mixing model. The first approach relies on an exact algebraic map between conservative and reactive species for an instantaneous irreversible bimolecular reaction that allows to estimate reactive mixing based on experimental conservative transport data. The second approach is based on reactive random walk particle tracking simulations in the numerically determined flow field in the water phase. The third approach uses a dispersive lamella approach that accounts for the impact of flow heterogeneity on mixing in terms of effective dispersion coefficients, which are estimated from both experimental data and numerical random walk particle tracking simulations. We observe a significant increase in reactive mixing for decreasing saturation, which is caused by the stronger heterogeneity of the water phase and thus of the flow field. This is consistently observed in the experimental data and the direct numerical simulations. The dispersive lamella model, parameterized by the effective interface width, provides robust estimates of the evolution of the product mass obtained from the experimental and numerical data.